Numerical Methods for Stochastic Partial Differential Equations with White Noise

Preface.- Prologue.- Brownian Motion and Stochastic Calculus.- Numerical Methods for Stochastic Differential Equations.- Part I Stochastic Ordinary Differential Equations.- Numerical Schemes for SDEs with Time Delay Using the Wong-Zakai Approximation.- Balanced Numerical Schemes for SDEs with non-Lipschitz Coefficients.- Part II Temporal White Noise.- Wiener Chaos Methods for Linear Stochastic Advection-Diffusion-Reaction Equations.- Stochastic Collocation Methods for Differential Equations with White Noise.- Comparison Between Wiener Chaos Methods and Stochastic Collocation Methods.- Application of Collocation Method to Stochastic Conservation Laws.- Part III Spatial White Noise.- Semilinear Elliptic Equations with Additive Noise.- Multiplicative White Noise: The Wick-Malliavin Approximation.- Epilogue.- Appendices.- A. Basics of Probability.- B. Semi-analytical Methods for SPDEs.- C. Gauss Quadrature.- D. Some Useful Inequalities and Lemmas.- E. Computation of Convergence Rate.